Discrete geometry, computational geometry


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We study different frameworks that allow us to define, in discrete spaces, some fundamental geometrical and topological notions and transforms. Two aspects are highlighted in our work: mathematical rigor (proven properties) and algorithmic efficiency. In particular, we have developped a new framework called Critical Kernels, which is at present time the most general and powerful framework for the study and the design of parallel thinning operators. We also work on new ways to propose approximate and easily computable solutions, with bounded error, for NP-difficult problems on geometric data.